Denis Voskov

Fully compositional and thermal reservoir simulation

Abstract Fully compositional and thermal reservoir simulation capabilities are important in oil exploration and production. There are significant resources in existing wells and in heavy oil, oil sands, and deep-water reservoirs. This article has two main goals: (1) to clearly identify chemical engineering sub-problems within reservoir simulation that the PSE community can potentially make contributions to and (2) to describe a new computational framework for fully compositional and thermal reservoir simulation based on a combination of the Automatic Differentiation-General Purpose Research Simulator (AD-GPRS) and the multiphase equilibrium flash library (GFLASH). Numerical results for several chemical engineering sub-problems and reservoir simulations for two EOR applications are presented. Reservoir simulation results clearly show that the Solvent Thermal Resources Innovation Process (STRIP) outperforms conventional steam injection using two important metrics – sweep efficiency and oil recovery.

Compositional Space Parameterization: Theory and Application for Immiscible Displacements

Summary Thermodynamic equilibrium calculations in compositional flow simulators are used to find the partitioning of components among fluid phases, and they can be a time consuming kernel in a compositional flow simulation. We describe a tie-line-based compositional space parameterization (CSP) approach for dealing with immiscible gas-injection processes with large numbers of components. The multicomponent multiphase equilibrium problem is recast in terms of this parameterized compositional space, in which the solution path can be represented in a concise manner. This tie-line-based parameterization approach is used to speed up the phase behavior calculations of standard compositional simulation. Two schemes are employed. In the first method, the parameterization of the phase behavior is computed in a preprocessing step, and the results are stored in a table. During the course of a simulation, the flash calculation procedure is replaced by the solution of a multidimensional optimization problem in terms of the parameterized space. For processes where significant changes in pressure and temperature take place, this optimization procedure is combined with linear interpolation in tie-line space. In the second method, compositional space adaptive tabulation (CSAT) is used to accelerate the equation of state (EOS) computations associated with standard compositional reservoir simulation. The CSAT strategy takes advantage of the fact that, in gas injection processes, the solution path involves a limited number of tie-lines. The adaptively collected tie-lines are used to avoid redundant phase-stability checks in the course of a flow simulation. Specifically, we check if a given composition belongs to one of the tie-lines (or its extension) already in the table. If not, a new tie-line is computed and added to the table. The CSAT technique was implemented in a general-purpose research simulator (GPRS), which is designed for compositional flow simulation on unstructured grids. Using a variety of challenging models, we show that, for immiscible compositional processes, CSAT leads to significant speed up (at least a several-fold improvement) of the EOS calculations compared with standard techniques.

Compositional Space Parameterization: Multicontact Miscible Displacements and Extension to Multiple Phases

This paper (SPE 113492) was accepted for presentation at the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, 20–23 April 2008, and revised for publication. Original manuscript received for review 12 February 2008. Revised manuscript received for review 18 August 2008. Paper peer approved 21 August 2008. Summary We generalize the compositional space parameterization (CSP) approach, which was originally developed for immiscible twophase multicomponent problems, to multicontact miscible displacements. The tie-line based parameterization method improves both the accuracy of the phase-behavior representation as well as the efficiency of equation of state (EOS) computations in compositional flow simulation. For immiscible compositional simulation, compositional space adaptive tabulation (CSAT) can be used to avoid most of the redundant EOS calculations. Because the supercritical region cannot be parameterized using tie-lines, the original CSAT approach is not effective for modeling multicontact miscible gas injection processes. To deal with supercritical compositions, a supercritical state criteria (SSC) algorithm based on adaptive tabulation of the minimal critical pressure (MCP) tie-lines is proposed. For general-purpose simulation of miscible and immiscible compositional displacement processes, we combined the adaptive CSAT strategy in the region of tie-line extensions and the adaptive SSC scheme; we refer to the overall framework as CSAT. Results of several challenging tests of practical interest indicate that the general CSAT strategy is quite robust and that it leads to an order of magnitude gain in computational efficiency. We also describe the extension of the CSP framework for mixtures that form more than two phases.

An Extended Natural Variable Formulation for Compositional Simulation Based on Tie-Line Parameterization

A nonlinear formulation based on extension of natural variables set is proposed for modeling compositional two-phase flow in porous media. The focus here is on numerical general-purpose simulation using the fully implicit method. In the formulation, the phase fraction and the saturation change “continuously” in the immiscible region of the compositional space (i.e., sub-critical region). Inside the two-phase region, these variables are identical to the saturation and phase-fraction of the standard approach. In the single-phase regions, however, these saturation-like and phase-fraction-like variables can become negative, or larger that unity. We demonstrate that when this variable set is used, the equation-of-state (EoS)-based thermodynamic equilibrium computations are resolved completely within the global Newton loop. That is, need not to separate things into phase stability and flash computations. Compared to the standard natural variables approach, the number of global Newton iterations grows only slightly, but overall, the new approach leads to more efficient simulations. Moreover, the continuous variation of both the saturation and phase fraction across phase boundaries results in improved behavior of the nonlinear (Newton) solver. Two different strategies are used to deal with the densities. The first scheme honors the nonlinear dependence of the overall density on phase fractions and saturation, and the second employs a linearized relation for the overall density. Both schemes are compared with the standard natural variables formulation using several challenging compositional problems.

Effect of time stepping strategy on adjoint-based production optimization

The adjoint gradient method is well recognized for its efficiency in large-scale production optimization. When implemented in a sequential quadratic programming (SQP) algorithm, adjoint gradients enable the construction of a quadratic approximation of the objective function and linear approximation of the nonlinear constraints using just one forward and one backward simulation (with multiple right-hand sides). In this work, the focus is on the performance of the adjoint gradient method with respect to the adaptive time step refinement generated in the underlying forward simulations. First, we demonstrate that the mass transfer in reservoir simulation and, as a consequence, the net-present value (NPV) function are more sensitive to the degree of the time step refinement when using production bottom-hole pressure (BHP) controls than when using production rate controls. Effects of this sensitivity on optimization process are studied using six examples of uniform time stepping with different degrees of refinements. By comparing those examples, we show that corresponding optimal solutions for target production BHPs deviate at early stages of the optimization process. It indicates an inconsistency in the evaluation of the adjoint gradients and NPV function for different time step refinements. Next, we investigate the effects of this inconsistency on the results of a constrained production optimization. Two strategies of nonlinear constraints are considered: (i) nonlinear constraints handled in the optimization process and (ii) constraints applied directly in forward simulations with a common control switch procedure. In both strategies, we observe that the progress of the optimization process is greatly influenced by the degree of the time step refinement after control update. In the case of constrained simulations, the presence of control switches combined with large time steps after control update forces adaptive refinement to vary the time step size significantly. As a result, the inconsistency of the adjoint gradients and NPV values provoke an early termination of the SQP algorithm. In the case of constrained optimization, the inconsistencies in gradient evaluations are less significant, and the performance of the optimization process is governed by a satisfaction of nonlinear constraints in SQP algorithm.

Tie-Simplex Parameterization for EOS-Based Thermal Compositional Simulation

Summary Thermodynamic equilibrium computations are usually the most time-consuming component in compositional reservoir flow simulation. A compositional space adaptive tabulation (CSAT) approach was developed as a preconditioner for equation of state (EOS) computations in isothermal compositional simulation. The compositional space is decomposed into sub- and supercritical regions. In the subcritical region, we adaptively parameterize the compositional space using a small number of tie-lines, which are assembled into a table. The critical surface is parameterized and used to identify supercritical compositions. The phase-equilibrium information for a composition is interpolated as a function of pressure using the tie-line table. We extend the CSAT approach to thermal problems. Given an overall composition at a fixed temperature, the boundary between sub- and supercritical pressures is represented by the critical tie-line and the corresponding minimal critical pressure (MCP). A small set of subcritical tie-lines is computed and stored for a given temperature. This process is repeated for the pressure and temperature ranges of interest, and a coarse (regular) tie-line table is constructed. Close to the critical boundary, a refined tie-line table is used. A combination of regular and refined interpolation improves the robustness of the tie-line search procedure and the overall efficiency of the computations. Several challenging problems, including an unstructured heterogeneous discrete fracture field model with 26 components, are used to demonstrate the robustness and efficiency of this general tie-line-based parameterization method. Our results indicate that CSAT provides accurate treatment of the near-critical region. Moreover, the computational efficiency of the method is at least an order of magnitude better than that of standard EOS-based reservoir simulation approaches. We also show the efficiency gains relative to standard techniques as a function of the number of gridblocks in the simulation model.

A coarse-scale compositional model

In subsurface flow modeling, compositional simulation is often required to model complex recovery processes, such as gas/CO 2 injection. However, compositional simulation on fine-scale geological models is still computationally expensive and even prohibitive. Most existing upscaling techniques focus on black-oil models. In this paper, we present a general framework to upscale two-phase multicomponent flow in compositional simulation. Unlike previous studies, our approach explicitly considers the upscaling of flow and thermodynamics. In the flow part, we introduce a new set of upscaled flow functions that account for the effects of compressibility. This is often ignored in the upscaling of black-oil models. In the upscaling of thermodynamics, we show that the oil and gas phases within a coarse block are not at chemical equilibrium. This non-equilibrium behavior is modeled by upscaled thermodynamic functions, which measure the difference between component fugacities among the oil and gas phases. We apply the approach to various gas injection problems with different compositional features, permeability heterogeneity, and coarsening ratios. It is shown that the proposed method accurately reproduces the averaged fine-scale solutions, such as component overall compositions, gas saturation, and density solutions in the compositional flow.

Heavy oil recovery efficiency using SAGD, SAGD with propane co-injection and STRIP-SAGD

Abstract Primary oil recovery methods in heavy oil basins generally extract 5–10% of the available resource, with the vast majority left in the ground and recoverable only through Enhanced Oil Recovery (EOR) methods. Traditional EOR methods, such as SAGD and solvent-assisted SAGD, generate steam in surface facilities and inject it underground to mobilize the oil for production. However, these methods can have considerable energy losses that significantly impact process performance. In contrast, the Solvent Thermal Resource Innovation Process (STRIP) technology, which uses down hole combustion of methane to produce CO 2 and steam, reduces the operating and capital costs of surface facilities, saving more than 50% of the energy typically required for thermal production. In this work, simulations of conventional SAGD, SAGD with a non-condensing solvent (propane), and STRIP-SAGD for a typical bitumen reservoir in the Fort McMurray region in Alberta, Canada were performed using the combined software system ADGPRS/GFLASH. SAGD simulations used steam injection with a quality of 0.8 while STRIP simulations injected a vapor–liquid mixture with a quality of 0.8. Furthermore, both solvent-based EOR methods required longer operation periods than conventional SAGD to recover a similar amount of oil. However, when compared on the basis of cumulative oil produced for the same overall energy input, it is shown that STRIP-SAGD recovered more oil per kJ of energy input to the reservoir than either SAGD or SAGD with propane co-injection.

Phase-state identification bypass method for three-phase thermal compositional simulation

In this paper, we propose a strategy to bypass the phase identification of fluid mixtures that can form three, or more, phases. The strategy is used for reservoir simulation of multicomponent, three-phase, thermal compositional displacement processes. Since the solution path in compositional space is determined by a limited number of “key” tie-simplexes, the proposed “bypass” method uses information from the parameterized tie-simplexes and their extensions. The tie-simplex parameterization is performed in the discrete phase-fraction space. Once the phase-fraction space is discretized, a conventional three-phase flash is used adaptively to compute the phase states at the discretization nodes. If all discretization vertices of a given discrete cell, in phase-fraction space, have the same phase state, then this state is assigned to the entire cell and expensive flash calculations are bypassed. We demonstrate the robustness and efficiency of our phase identification bypassing strategy for several cases with three-phase flow, including a six-component ES-SAGD (enhanced solvent SAGD) model.

Unified thermo-compositional-mechanical framework for reservoir simulation

We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositional-mechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems.